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Sandbox Physics

Optics 062 · Diffraction, Fourier optics, and computational imaging

Optical Fourier Processor

An independently initialized three-dimensional apparatus connects Single-lens Fourier plane, Four-f spatial filter, Correlation and stripe removal. Two dimensional physical controls, direct probe dragging, a detector trace, and three quantitative checks are recalculated from the stated equation.

Interactive modelOptical Fourier Processor
Primary prediction P1\mathcal P_10.500.50
Physical scale P2\mathcal P_250%50\%
Limit check V\mathcal V0.00π0.00\pi
Model regimevalid model regime\text{valid model regime}

Physics tutorial

How to investigate Optical Fourier Processor

BackgroundOptical Fourier Processor is one independently initialized apparatus with three linked investigations: Single-lens Fourier plane, Four-f spatial filter, Correlation and stripe removal. Its two controls—Filter cutoff and Object frequency—feed the governing relation Uout=F−1 ⁣{H F[Uin]}U_{\mathrm out}=\mathcal F^{-1}\!\left\{H\,\mathcal F[U_{\mathrm in}]\right\}. Scalar, paraxial, or sampled-field assumptions are stated by the validity indicator; vector and nonparaxial effects are outside that boundary.

Why it mattersHow does moving one filter in a Fourier plane rewrite edges, blur, and repeated texture in an image?

Start with the essentials

Focus question
How does moving one filter in a Fourier plane rewrite edges, blur, and repeated texture in an image?
One-sentence intuition
The detector curve and all three numerical readouts are recomputed from Uout=F−1 ⁣{H F[Uin]}U_{\mathrm out}=\mathcal F^{-1}\!\left\{H\,\mathcal F[U_{\mathrm in}]\right\}. Geometry and glow are presentation encodings; the equation, units, conservation or limit check, and validity indicator are the quantitative evidence.

Core mathematical model

Governing relation

Uout=F−1 ⁣{H F[Uin]}U_{\mathrm out}=\mathcal F^{-1}\!\left\{H\,\mathcal F[U_{\mathrm in}]\right\}

The implementation evaluates this relation with dimensional inputs and an executable analytic or numerical benchmark. Scalar, paraxial, or sampled-field assumptions are stated by the validity indicator; vector and nonparaxial effects are outside that boundary.

Common difficulties

Mistaking glow for measured power

Typical misconceptionA brighter cinematic trail must represent proportionally more optical power.

Better mental modelUse the detector and normalized readouts for comparison. Glow is deliberately nonlinear so weak structure stays visible.

Run the experiment

  1. 01

    Scene 1: Single-lens Fourier plane

    Select Single-lens Fourier plane. Sweep Filter cutoff, hold Object frequency fixed, and then reverse the roles. Drag the stage probe to repeat the first sweep directly.

    What to observe: Read the primary prediction, physical scale, limit check, and validity indicator together. Record where the approximation boundary changes.
  2. 02

    Scene 2: Four-f spatial filter

    Select Four-f spatial filter. Sweep Filter cutoff, hold Object frequency fixed, and then reverse the roles. Drag the stage probe to repeat the first sweep directly.

    What to observe: Read the primary prediction, physical scale, limit check, and validity indicator together. Record where the approximation boundary changes.
  3. 03

    Scene 3: Correlation and stripe removal

    Select Correlation and stripe removal. Sweep Filter cutoff, hold Object frequency fixed, and then reverse the roles. Drag the stage probe to repeat the first sweep directly.

    What to observe: Read the primary prediction, physical scale, limit check, and validity indicator together. Record where the approximation boundary changes.